This paper deals with the dynamic response of thin circular clamped GLARE plates subjected to low velocity impact. Using a spring-mass model, the differential equations of motion are derived and solved analytically. Internal damage arising from delamination is considered. No other solution of this problem is known to the authors.

Published formulas for the static indentation of GLARE plates are employed during loading stages of impact [1,2]. Considering that aluminium layers are in a state of membrane yield, an equation for the unloading path is derived and used during unloading impact stage. We distinguish three stages of motion representing the impact phenomenon. During the first stage, the impactor deforms the plate until delamination damage occurs. The second stage starts after delamination up to the maximum plate deformation while the final stage starts from this position and ends when impact load becomes zero.

Analytical expressions for calculation of load - time, position - time, velocity - time and kinetic energy - time histories are derived by solving the differential equations of motion. Furthermore, the delamination position, the maximum plate deformation and the position where impact load becomes zero are predicted analytically. Also, expressions for calculating maximum impact load and total impact duration are given. All these quantities are of great interest for impact studies.

The derived expressions are applied successfully to GLARE 4-3/2. The predicted impact variables are compared with published experimental data and a close agreement is found (maximum impact load is within 3% of the experimental, the maximum impact load time is within 4% of the experimental, the total impact duration is within 3% of the experimental).

The theoretical model presented can be used for design of GLARE plates subjected to low velocity impact and for comparison of the dynamic response of different GLARE grades when subject to low velocity impact.

Also, the model is expected to predict satisfactorily the dynamic response of circular plates consisting of other advanced hybrid material systems of alternating metal layers bonded to fiber-reinforced polymer layers when subjected to low velocity impact, provided that our assumptions remain valid.

1

G.J. Tsamasphyros, G.S. Bikakis, "Analytical modeling of circular GLARE laminated plates under lateral indentation", Advanced Composites Letters, 18(1), 11-19, 2009.

2

G.J. Tsamasphyros, G.S. Bikakis, "Finite element modeling and analytical simulation of circular GLARE fiber-metal laminates subjected to lateral indentation", Journal of the Serbian Society for Computational Mechanics, 3(2), 67-80, 2009.

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